arXiv:1511.09408v2 [astro-ph.HE] 21 Jan 2016
Published in JCAP as doi: 10.1088/1475-7516/2016/01/037
Search for correlations between the
arrival directions of IceCube
neutrino events and ultrahigh-energy
cosmic rays detected by the Pierre
Auger Observatory and the
Telescope Array
The IceCube, Pierre Auger and Telescope Array Collaborations
Abstract. This paper presents the results of different searches for correlations between
very high-energy neutrino candidates detected by IceCube and the highest-energy cosmic rays measured by the Pierre Auger Observatory and the Telescope Array. We first
consider samples of cascade neutrino events and of high-energy neutrino-induced muon
tracks, which provided evidence for a neutrino flux of astrophysical origin, and study
their cross-correlation with the ultrahigh-energy cosmic ray (UHECR) samples as a function of angular separation. We also study their possible directional correlations using
a likelihood method stacking the neutrino arrival directions and adopting different assumptions on the size of the UHECR magnetic deflections. Finally, we perform another
likelihood analysis stacking the UHECR directions and using a sample of through-going
muon tracks optimized for neutrino point-source searches with sub-degree angular resolution. No indications of correlations at discovery level are obtained for any of the
searches performed. The smallest of the p-values comes from the search for correlation
between UHECRs with IceCube high-energy cascades, a result that should continue to
be monitored.
Keywords: neutrino experiments, ultra high energy cosmic rays, cosmic ray experiments, neutrino astronomy
Contents
1 Introduction
1
2 The observatories and data sets
2.1 The IceCube Neutrino Observatory
2.1.1 High-energy starting events (HESE)
2.1.2 High-energy through-going muons
2.1.3 4-year point-source sample
2.2 The Pierre Auger Observatory and its data sample
2.3 Telescope Array and its data sample
4
4
4
5
5
7
7
3 Magnetic deflections of UHECRs
8
4 UHECR correlation analyses with high-energy cascades and high-energy
tracks
10
4.1 Cross-correlation analysis with high-energy cascades and high-energy tracks 10
4.2 Stacking analysis with high-energy cascades and high-energy tracks
12
4.3 Results
14
5 Stacking search with the 4 year point-source sample
5.1 Method and discovery potential
5.2 Results
18
18
21
6 Conclusions
21
A Neutrino
27
1
Introduction
The origin of the ultrahigh-energy cosmic rays is one of the main open questions in
high-energy astrophysics. It is likely that they are accelerated in astrophysical objects,
since more exotic scenarios for their origin, such as the top-down models, are strongly
constrained by stringent limits on the flux of primary photons at such energies [1, 2].
However, their sources still remain undiscovered after five decades of experimental efforts
that have culminated in the two largest UHECR experiments ever built, the Pierre
Auger Observatory [3, 4] and the Telescope Array [5], in the Southern and Northern
hemispheres, respectively. The two experiments, which measure UHECRs through the
detection of extensive air showers produced in the Earth’s atmosphere, have collected in
total more than 300 events with energies in excess of ∼ 50 EeV (where 1 EeV ≡ 1018 eV).
These energies are well within the region of very significant cosmic-ray flux suppression
observed by both experiments [6, 7]. If this suppression were due to the degradation of
the cosmic-ray (CR) energies by their interactions with the cosmic radiation backgrounds
–1–
[8], one would expect that the sources of such energetic CRs are relatively nearby, at
distances shorter than ∼ 200 Mpc. However, the results of several studies of UHECR
arrival direction distributions [9, 10] have shown no significant small-scale anisotropy and
have not allowed the establishment of statistically-significant correlations with nearby
astrophysical sources.
The identification of UHECR sources by correlation analyses is a challenging task.
Since UHECRs are mostly charged particles, their trajectories from their sources to
the Earth are deviated by magnetic fields, most notably by the Galactic field. The
deviations depend on the energy and charge of the cosmic ray: while at energies above
50 EeV they may be of order of a few degrees in the case of protons, such deviations
would be much larger for nuclei of the same energy but having a larger charge. This
situation is further complicated by the facts that there are still large uncertainties in the
modeling of magnetic fields (see [11, 12] and references therein) and that the UHECR
mass composition at energies above 50 EeV is still largely unexplored [13, 14].
Further, UHECRs accelerated in astrophysical sources are naturally expected to
produce high-energy photons and neutrinos in interactions with the ambient matter and
radiation. In contrast to UHECRs, photons and neutrinos are not subject to magnetic
deflections in their propagation to the Earth and hence they point directly to their
sources. However, high-energy photons may also be produced in purely leptonic processes, and hence may be unrelated to hadronic CRs. Moreover, photons at energies
exceeding a few TeV can be significantly attenuated by e+ e− -pair production in interactions with the Cosmic Microwave Background (CMB) and other radiation backgrounds
as they propagate from faraway sources. On the other hand, neutrinos interact with
matter very weakly, so that they travel essentially unattenuated, and hence are excellent
tracers of the sources of cosmic rays. Due to the challenge of neutrino detection, neutrino astronomy has however become viable only very recently, thanks to the discovery
by the IceCube neutrino telescope [15] of a flux of extraterrestrial high-energy neutrinos
extending up to at least 2 PeV.
The observations of the highest-energy events, on the one hand in neutrinos by
IceCube and on the other, UHECRs, by the Auger Observatory and the Telescope Array,
set the stage for a joint analysis of the three Collaborations presented in this paper,
namely the search for a possible association between the IceCube neutrinos and the
UHECRs. Some analyses searching for possible correlations have been presented in
[16–18], but using smaller data sets.
Attempting to exploit the IceCube neutrino observations to identify the sources of
UHECRs is motivated by several reasons. First, the arrival directions of the IceCube
high-energy sample, in which a cosmic component has been identified [15], is consistent
with an isotropic distribution and therefore with the hypothesis of an extragalactic origin
for the bulk of the events, although the presence of a Galactic component is possible.
Second, the inferred diffuse flux of astrophysical neutrinos, with energies between 30 TeV
and 2 PeV, is at the level of the Waxman-Bahcall flux [19]. This is the upper limit for
the extragalactic neutrino flux calculated assuming that UHECRs are protons escaping
from optically thin sources with an injection spectrum scaling as E −2 and normalized to
–2–
the measured UHECR flux above EeV energies. Clearly, if the sources are not opticallythin, or if the injection spectrum differs from E −2 , or the UHECRs are not protons, the
upper limit on the flux would be considerably modified [20].
If neutrinos result from the decays of pions produced in pγ or pp processes, they
would carry about 3–5% of the proton energy. Hence, the neutrinos observed by IceCube
with energies of 30 TeV to 2 PeV would have been produced in this case by protons with
PeV–100 PeV energies. Although these energies are much smaller than those of the
UHECRs considered here, the third argument for our analysis is based on the fact that
it is only at the highest energies that CR trajectories could point to the sources, while
at much lower energies CRs diffuse and may not even arrive to the Earth from faraway
sources. Since UHECR sources will also produce lower energy CRs, it is possible that
they are the same sources that produced the observed neutrinos. One should keep
in mind, however, that there may also be sources able to produce the PeV neutrinos
but which do not accelerate CRs up to ultrahigh-energies. We also note that electron
antineutrinos produced in the β decay of neutrons (or of radioactive nuclei produced in
photo-disintegration processes) would carry about 4 × 10−4 of the energy of the parent
nucleon, and hence PeV neutrinos could in principle also arise from EeV neutrons.
In this paper we present several searches for correlations between the arrival directions of UHECRs detected by the Auger Observatory and by the Telescope Array, and of
different sets of events observed by the IceCube Neutrino Observatory. The main characteristics of the three detectors, and their respective data sets, are described in Section
2. The Auger and Telescope Array samples include 231 events with E ≥ 52 EeV and 87
with E ≥ 57 EeV, respectively. The IceCube data sets that we consider, obtained using
different selection criteria, comprise 39 cascades (signatures of charged-current νe interactions as well as neutral-current interactions of all flavors) and 7 high-energy tracks
(signatures of charged-current νµ interactions) of the so-called ‘High Energy Starting
Events’ (HESE) [15, 21, 22], as well as 9 high-energy muon tracks whose extraterrestrial
origin is highly probable [23]. We also exploit the so-called point-source sample of about
400,000 tracks with a sub-degree angular resolution [24].
The search for correlations between neutrinos and UHECRs is not straightforward.
On the one hand, as noted above, due to the magnetic deviations discussed in Section 3,
the UHECR arrival directions do not exactly correspond to the source positions. On
the other hand, the neutrino HESE cascade events are characterized by a large angular
uncertainty. Moreover, the IceCube samples are not exempt from backgrounds due to
atmospheric secondary particles. In particular, the point-source sample is largely dominated by atmospheric muons in the Southern hemisphere and by atmospheric neutrinos
in the Northern one. To account for these aspects, three different analyses have been devised. Two analyses use the HESE and high-energy muon samples (Section 4). The first
one is a cross-correlation analysis where the number of pairs between CRs and the highenergy neutrino sample is evaluated within a large range of angular windows, from 1◦ up
to 30◦ . The second one adopts a stacking likelihood analysis, summing the contributions
from the different sources. In this case, it is the arrival directions of the neutrinos that
are being stacked. Plausible UHECR magnetic deflections and the neutrino point-spread
–3–
functions are accounted for, together with the possible backgrounds. A third analysis
uses a likelihood method applied to the point-source sample (Section 5). We note that
the details of the analyses (angular scales explored, data samples considered, null hypotheses) were selected, as discussed in Sections 4.1, 4.2 and 5.1, before unblinding the
analyses (see also [25]), while some a posteriori cross checks are also mentioned. Finally,
we conclude in Section 6.
2
The observatories and data sets
2.1
The IceCube Neutrino Observatory
The IceCube Observatory is a km3 -sized Cherenkov detector embedded in the ice at
the geographic South Pole [26]. Optimized to detect neutrinos above ∼ 100 GeV energies, it consists of 5160 photomultiplier tubes (PMTs) along 86 cables (called ‘strings’)
instrumented between depths of 1450 and 2450 m beneath the surface of the ice sheet.
Each PMT is housed in a digital optical module (DOM), consisting of a pressure-resistant
sphere with on-board digitization and Light Emitting Diodes (LEDs) for calibration [27].
The DOMs detect Cherenkov photons emitted by charged leptons that traverse the ice
volume [28]. Starting in the year 2005, the detector ran in partial configurations consisting of 9, 22, 40, 59 and 79 strings until its completion in December 2010.
2.1.1
High-energy starting events (HESE)
In 2013, IceCube reported the first evidence for a high-energy neutrino flux of extraterrestrial origin from a search carried out on data collected between May 2010 and May
2012 in the 79-string and full 86-string configurations of the detector [15]. That search,
targeting high-energy neutrinos interacting within the IceCube detector, was later updated to include two more years of data taken with the full 86-string configuration,
extending the observation period to May 2014 [21, 22]. These searches have consistently demonstrated the existence of an astrophysical flux of neutrinos at the level of
Eν2 φ(Eν ) ∼ 10−8 GeV cm−2 s−1 sr−1 per flavor, emerging above atmospheric neutrinos
starting at around 100 TeV and extending to the PeV range. The hypothesis of a purely
atmospheric explanation of the neutrino events collected during 4 years has been rejected
at around 6.5σ. However, the 54 events consisting of 39 cascades and 15 track-like events
have shown no significant directional clustering, leaving unanswered the question of their
origin [21, 22].
The median angular resolution of the events containing muon tracks is around 1◦ ,
while the resolution of cascade-like events is around 15◦ [15]. The expected atmospheric
background for the HESE sample is predominantly track-like atmospheric muons not
vetoed by external layers of DOMs and sneaking in through the region called the ‘dust
layer’ (where dust obscures the transparency of ice) and from atmospheric νµ chargedcurrent interactions from the Northern hemisphere. We have therefore not used all the
detected track-like events, but only the 7 that are more likely to be of extraterrestrial
origin due to their high energies and/or arrival directions. Atmospheric neutrinos from
–4–
the Southern hemisphere are accompanied by muons from the same shower and this
background is greatly reduced by the event selection using a muon veto [21].
Within this paper these 39 cascade events and 7 track-like events are referred to as
‘high-energy cascades’ and ‘HESE tracks’, respectively, and their properties are listed in
Table 4 and Table 5 in the Appendix.
2.1.2
High-energy through-going muons
A data sample of 35,000 through-going muons from the Northern sky was selected from
events recorded between May 2010 and May 2012 in a search for a diffuse up-going
νµ flux [23]. While the majority of these events originate from neutrinos produced by
cosmic-ray interactions in the Earth’s atmosphere, at the highest energies a clear excess
was observed. The hypothesis that the excess is of atmospheric origin was rejected at
the 3.7σ confidence level [23]. This excess is compatible with the sum of the predicted
muon neutrinos of atmospheric origin and an astrophysical flux consistent with the flux
resulting from the HESE analysis. This deviation from the expectation that all events are
of atmospheric origin occurs at the highest energies, where 9 events have been detected.
These events (which are available in [29]) are listed in Table 5 and have a median angular
resolution of around 1◦ . The combination of these events with the 7 selected HESE tracks
is referred to as ‘high-energy tracks’.
2.1.3
4-year point-source sample
High-energy muons have long tracks within IceCube and they can be reconstructed with
a median angular resolution smaller than 1◦ , and hence they have good sensitivity for
point-source searches. The corresponding effective volume to neutrino-induced muon
events can be larger than the instrumented volume since the interaction vertex of the
neutrino does not have to be contained within the detector. Four dedicated samples of
such events have been isolated in three years of operation of IceCube in the incomplete
40-, 59- and 79-string configurations [30, 31] as well as in one year of operation of the
completed 86-string detector [24]. Note that 7 events out of the 9 high-energy throughgoing muons described in Section 2.1.2 are contained in the point-source data set.
The angular resolution of this sample has improved over the years, benefiting from
the larger instrumented volumes achieved as the number of strings was increasing as well
as from improvements in the reconstruction methods (see Figure 1). These samples are
dominated by muons from charged-current interactions of atmospheric νµ (and ν̄µ ) in
the Northern hemisphere (up-going data) and muons produced by interactions of cosmic
rays with the Earth’s atmosphere in the Southern hemisphere (down-going data). In
the Northern sky, the effective area of the detector, determined by the analysis cuts
and the opacity of the Earth for neutrinos with energies above ∼ 100 TeV, leads to a
sample of events peaked in the 1 TeV – 1 PeV range. In the Southern sky the sensitivity
is in the 100 TeV – 100 PeV range (see Figure 2) due to the overwhelming background
of atmospheric muons that needs to be reduced by imposing a higher threshold cut on
the energy proxy.
–5–
Median angular resolution [°]
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
102
IC86
IC79
IC59
IC40
ν-µ Opening angle
103
104
105
106
107
108
Eν [GeV]
Figure 1. Muon neutrino angular resolution for the Northern sky (up-going events), defined
as the median of the angle between the true neutrino direction and the reconstructed muon
direction. The resolution is given for different analyzed samples as a function of the neutrino
energy after all cuts used to select the final samples for the neutrino point-source searches. The
kinematic angle between the muon and the neutrino is also shown with a dashed line.
1.0
90% E−2.0
90% E−2.3
90% E−2.7
sin(δ)
0.5
0.0
−0.5
−1.0 2
10
103
104
105 106
Eν (GeV)
107
108
109
Figure 2. Neutrino energy interval containing 10% to 90% of the simulated signal events
for different spectra and declinations for the four-year combined point-source samples after all
analysis cuts are applied.
–6–
2.2
The Pierre Auger Observatory and its data sample
The Pierre Auger Observatory [3, 4] (Malargüe, Argentina, 35.2◦ S, 69.5◦ W, 1400 m
a.s.l.) combines a large surface detector (SD) with an air-fluorescence detector (FD) to
observe, in a complementary way, extensive air showers generated by ultrahigh-energy
cosmic rays. The SD is composed of an array of 1660 water-Cherenkov stations spread
over an area of about 3000 km2 . It measures, with a duty cycle of nearly 100%, the
particles (mainly muons, electrons and photons) reaching ground level. The FD, comprising 27 telescopes at four sites, overlooks the surface array and observes, with a duty
cycle close to 15%, the fluorescence light emitted by nitrogen molecules excited by the
particles from the air showers.
The data set used in the present work consists of 231 cosmic-ray events with zenith
angle θ ≤ 80◦ and energy ECR ≥ 52 EeV recorded by the SD from January 1, 2004 up
to March 31, 2014 1 . These events satisfy a fiducial cut requiring their impact position
to be well-contained in the SD array. This ensures an accurate reconstruction of the
shower geometry and energy as well as a robust estimation of the exposure.
The arrival directions of these cosmic rays are determined from the relative arrival
times of the shower front in the triggered stations. The angular resolution, defined as
the radius around the true cosmic-ray direction that would contain 68% of the reconstructed shower directions, is better than 0.9◦ for the energies considered here [32]. The
energy estimate is obtained from the signals recorded by the SD stations [33, 34] and
is calibrated using ‘hybrid’ events (i.e., detected simultaneously by SD and FD) and
using the quasi-calorimetric energy determination obtained with the FD [35, 36]. The
statistical uncertainty in the energy determination is smaller than 12% for the energies
used here [34, 36]. The systematic uncertainty on the absolute energy scale is 14%.
At energies above 4 EeV the SD trigger is fully efficient, and the determination
of the exposure is purely geometrical [37]. For the time period considered and for the
applied energy and zenith angle selection, it amounts to 66,452 km2 sr yr. The adopted
zenith-angle selection allows the field of view of the Observatory to extend from −90◦
to +45◦ in declination.
2.3
Telescope Array and its data sample
The Telescope Array (TA) is situated in Utah, USA (39.3◦ N, 112.9◦ W, 1400 m a.s.l.).
It consists of 507 plastic scintillator detectors, each of 3 m2 in area, located on a 1.2 km
square grid and covering an area of approximately 700 km2 (for further details see [5]).
The atmosphere over the surface array is viewed by 38 fluorescence telescopes arranged
in 3 stations. The detector has been fully operational since March 2008.
In this analysis, we use surface-detector data recorded between May 11, 2008 and
May 4, 2014. For the reconstructed events, the energies determined by the SD array
were renormalized by 1/1.27 to match the SD energy scale to that of the fluorescence
detector, which was determined calorimetrically [7]. Of these events, 87 met the following
1
The list of events, together with a more detailed description of their selection and reconstruction,
can be found in [9].
–7–
criteria: (1) each event triggered at least four SD counters; (2) the zenith angle of the
event arrival direction was less than 55◦ ; and (3) the reconstructed energy was greater
than 57 EeV. The event-selection criteria described above are the same as in Ref. [38] and
were optimized to increase the observed number of cosmic rays. The angular resolution
of these events is about 1.5◦ , while the energy resolution is ∼ 20%. The systematic
uncertainty on the energy scale is 22% [7].
To conclude the description of the data, a remark is in order. As already mentioned,
the absolute energy scale of UHECRs may contain a systematic error which may be, in
principle, different for the two experiments. In accordance with the findings of the TAAuger Energy Spectrum working group [39], the UHECR spectra measured by Auger
and TA may be made coincident in the region around 1019 eV (the ‘ankle’ region) by
up-shifting the Auger energies (equivalently, down-shifting the TA energies) by ∼ 13%.
Assuming that the relative shift is energy-independent, and to make the energy scales
compatible, we choose to down-shift the TA energies by 13% in the likelihood analyses
presented here. Note that assuming lower energies is a conservative choice with respect
to the assumed magnetic deflections for the analyses since the deflections grow as the
energy decreases. In view of its relatively small magnitude, the overall effect of this shift
on the analyses is minor.
3
Magnetic deflections of UHECRs
The deflections in the magnetic fields to which, unlike neutrinos, cosmic rays are subject,
are crucial in determining the sensitivity of the analyses presented in this paper and any
interpretation of the results requires their understanding. The cosmic magnetic fields
that deflect the UHECR trajectories are naturally separated into the Galactic and the
extragalactic fields. Of these, the extragalactic fields are the least known. The Faraday
rotation measurements of extragalactic sources indicate that the extragalactic fields are
smaller than ∼ 10−9 G [40–42]. In this scenario, for a correlation length smaller than
1 Mpc, the deflections of protons of energy 1020 eV over a distance of 50 Mpc are smaller
than 2◦ .
The Galactic magnetic field can be further divided into regular and turbulent components. The regular part of the Galactic magnetic field is expected to give a dominant
contribution to the UHECR deflections. There are several models of the regular Galactic
field in the literature (see, e.g., [12] for a recent review). While the averages of the magnitudes of the deflections across the sky predicted in these models are similar, individual
deflections in a given direction of the sky vary substantially, so that reliable predictions
have not yet been achieved. To get an idea of the expected magnitude of the deflections,
a set of 105 random cosmic-ray events was simulated following the Auger and TA exposures, weighted in a proportion corresponding to the actual number of events in the
data sets of each experiment that we consider in this work. For each of these events we
computed the deflection angle according to two recent Galactic magnetic field models
[43, 44], assuming the primary CR to be a proton and its energy to be 1020 eV. The
corresponding distributions are shown in Figure 3. The median deflections from the two
–8–
Frequency [arb. units]
0.5
JF2012
PT2011
0.4
0.3
0.2
0.1
0
0
2
4
6
8
Deflection [°]
10
12
Figure 3. Distribution of UHECR deflections in two Galactic magnetic field models marked
PT2011 [43] and JF2012 [44] for the regular component. The energies of actual UHECRs are
renormalized to show the distributions for E/Z = 100 EeV. The double-peak structure is mostly
due to the fact that UHECRs from different Galactic hemispheres undergo different deflections.
models were found to be of the same order, ∼ 3◦ in both cases and having a rather wide
distribution.
Additionally, the cosmic rays are also deflected in the turbulent Galactic magnetic
field. There are several estimates of these deflections in the literature [45]. In all cases
the contribution due to the turbulent fields was found to be sub-dominant as compared
to that due to the regular field.
Apart from the magnetic field, the magnitude of the deflections also depends on
the composition of UHECRs. The current measurements of the UHECR composition at
the highest energies are still uncertain [13, 14], so that the assumed CR deflections are
uncertain too.
In summary, it appears unlikely that typical UHECR deflections at E = 1020 eV are
smaller than 2 − 3◦ , but may be significantly larger in the case of a heavier composition.
In particular, if the deflections are not too large, they scale approximately as Z/E,
where Z is the atomic number. In view of these large uncertainties, when considering
likelihood tests we perform the analyses for benchmark deflection values, parameterized
by the deflection D of a proton at E = 1020 eV. For simplicity, we model individual
deflections as a random variable with a 2-dimensional Gaussian distribution with the
energy-dependent width
σMD (E) = D × 100 EeV/E.
(3.1)
We consider test values of D = 3◦ , 6◦ and when possible, also of 9◦ , which are compat-
–9–
ible with the distributions for protons displayed in Figure 3 and may also account for
somewhat heavier cosmic rays.
4
UHECR correlation analyses with high-energy cascades and highenergy tracks
Two different analyses, a cross-correlation test and a stacking likelihood analysis, are
performed with the neutrino data sample of 39 high-energy cascade events (described in
Section 2.1.1) and the 16 high-energy tracks (7 from the sample described in Section 2.1.1
and the 9 described in Section 2.1.2). The total number of UHECRs is NCR = 318
(NAuger = 231 and NTA = 87). For the two analyses, cascades and tracks are considered
separately since, due to their different angular resolutions, the angular distance at which
a signal (if any) can be observed would be different.
4.1
Cross-correlation analysis with high-energy cascades and high-energy
tracks
If cosmic rays and neutrinos come from the same sources, then the angular separation
between their arrival directions would be related to the magnetic deflections suffered by
the cosmic rays, convoluted with the resolution in the determination of their respective
arrival directions. This angular distance is unknown a priori due to the poor knowledge of
the intervening magnetic fields and the uncertain value of the charges of cosmic rays. The
cross-correlation method consists of computing the number of UHECR-neutrino pairs as
a function of their angular separation α, np (α), and comparing it to the expectation from
an isotropic distribution of UHECR arrival directions. The angular scan performed in
this case is between 1◦ and 30◦ with a step of 1◦ . Due to this scan, the cross-correlation
method does not rely on any assumption about the exact value of the strength of the
magnetic deflections, unlike the likelihood method described in the following subsection
(though there is a large trial factor).
To estimate the significance of any excess, the pre-trial p-value is first computed by
evaluating for each angular distance scanned the fraction of isotropic simulations having
more pairs than the data. This is done by keeping the neutrino positions fixed and
simulating an isotropic distribution of the arrival directions of UHECRs arriving at the
Earth according to the corresponding geometric exposures of the Observatories. Then,
we find the angular scale for which this fraction is minimized, the minimum value of this
fraction being the pre-trial p-value. The post-trial p-value is calculated as the fraction
of simulations of isotropic arrival directions of cosmic rays that under a similar analysis
would give rise to a smaller pre-trial p-value than the one observed in the data.
Before applying the cross-correlation method to the data, its sensitivity and discovery potential are computed. The sensitivity is defined as the number of signal events,
ns , for which one would obtain a p-value of less than 50%, with respect to the isotropic
expectation, in 90% of the simulations. The discovery potential at, say, 3σ, is the number of signal events for which one would obtain a p-value corresponding to more than
3σ with 50% probability in repeated experiments. To obtain these quantities we perform simulations in which a number ns of cosmic-ray events are assumed to come from
– 10 –
sources. They are generated by smearing the positions of the neutrinos with a Gaussian
distribution with a standard deviation obtained from the median angular resolution of
each neutrino event, while the remaining NCR − ns events are assumed to be isotropic.
The sources are assumed to have equal apparent luminosity at Earth. To generate the
ns events, a decision is first made as to whether each event is a cosmic ray measured
by Auger or by TA, with a probability given by the fraction of the number of events
measured by each Observatory. A source position is then chosen with a probability given
by the relative exposure of the corresponding Observatory (shown in Figure 4).
The arrival direction of the ith UHECR event is obtained by smearing the source
position with a Gaussian with standard deviation σ(Ei ) calculated as:
q
2
2 (E ),
σ(Ei ) = σAuger,TA
+ σMD
(4.1)
i
where σAuger = 0.9◦ and σTA = 1.5◦ are the angular resolutions of Auger and TA,
respectively, and σMD (Ei ) is the magnetic deflection defined in Eq. (3.1). The UHECR
energy ECR is sampled according to the spectrum determined by Auger or TA in the
energy range of the UHECRs considered in this analysis, i.e., scaling as E −4.2 [46] and
E −4.5 [47], respectively.
The values obtained for the sensitivity (90% CL) and for the 3σ discovery potential
are listed in Table 1 in terms of ns , the total number of cosmic-ray signal events. They
imply for instance that for D = 3◦ a total number of around 15.9 cosmic-ray events
should originate on average from the directions of the neutrino tracks (or 93.9 from the
directions of the neutrino cascades) in order to reach a p-value corresponding to 3σ in
50% of the cases. Note that since in this case we are considering a total of 318 CR
directions, this would correspond to a situation in which ∼ 5% (∼ 30%) of the UHECRs
are required to have common sources with the neutrino tracks (cascades) in order to
reach a 3σ result if D = 3◦ (somewhat larger fractions are required for the D = 6◦ case).
Taking into account that there are 16 tracks and 39 cascades, we see that the average
number of required events per source is smaller for the tracks than for the cascades. This
is more evident for D = 3◦ since in this case the signal events happen to lie quite close
to the neutrino directions.
Table 1. Sensitivities and post-trial 3σ discovery potentials DP(3σ) for the cross-correlation
method in terms of ns , the total number of cosmic-ray signal events.
D
3◦
6◦
High-energy tracks
sensitivities DP(3σ)
7.0
15.9
11.1
25.3
– 11 –
High-energy cascades
sensitivities DP(3σ)
43.5
93.9
50.0
106.1
1
ω(δ)
0.8
0.6
0.4
0.2
0
Auger
TA
-80 -60 -40 -20
0
20 40 60 80
δ [°]
Figure 4. The geometrical relative exposures of the Pierre Auger Observatory and Telescope
Array as a function of declination. Both distributions have been normalized to unity at the
declinations where the exposure is maximum for each experiment. To simulate signal events,
the decision whether each event is a cosmic ray measured by Auger or by TA is done with a
probability given by the fraction of the number of events measured by each Observatory.
4.2
Stacking analysis with high-energy cascades and high-energy tracks
Stacking a set of sources is a well-known way of accumulating multiple weaker signals
to enhance the discovery potential. Even if the background is also stacked, a better
sensitivity can be achieved with this procedure than when looking at the same number
of sources separately [31]. Since neutrinos are neither deflected nor absorbed on their way
to Earth, here we stack the arrival directions of the neutrinos and search for coincident
sources of CRs.
The unbinned likelihood method is used in this analysis, with the log of the likelihood function defined as:
NAuger
ns i
NCR − ns i
log L(ns ) =
log
SAuger +
BAuger
NCR
NCR
i=1
N
TA
X
NCR − ns i
ns i
S +
BTA ,
+
log
NCR TA
NCR
X
(4.2)
i=1
where ns , the number of signal events, is the only free parameter, NCR = NAuger +NTA is
i
i are the signal probability density functions
the total number of UHECRs, SAuger
and STA
i
i
(PDFs) for Auger and for TA, respectively, and BAuger
and BTA
are the corresponding
background PDFs. The Auger signal PDF has the following form:
– 12 –
i
SAuger
(~ri , Ei )
= RAuger (δi ) ·
N
src
X
Sj (~ri , σ(Ei )),
(4.3)
j=1
where ~ri is the angular position of the ith UHECR event, RAuger (δi ) takes into account
the Auger detector response, e.g., the relative exposure for given event declination δi (see
Figure 4) and Nsrc is the number of stacked sources, 39 for the cascades and 16 for the
tracks. The last term, Sj (~ri , σ(Ei )) is the value of the normalized directional likelihood
map for the j th source (i.e., the j th neutrino) taken at ~ri and smeared with a Gaussian
with standard deviation σ(Ei ), defined in Eq. 4.1, with σAuger = 0.9◦ .
i
The signal PDF for Telescope Array STA
has the same form as Eq. 4.3, but the
relevant parts are replaced with the Telescope Array equivalents, namely RAuger (δi ) is
replaced by the Telescope Array relative exposure RTA (δi ) (see Figure 4) and the angular
resolution is σTA = 1.5◦ .
i
i , represent the probabilities of observing a
The background PDFs, BAuger
and BTA
cosmic ray from a given direction assuming an isotropic flux. Therefore they are taken
to be the Auger and TA normalized exposures (see Figure 4).
In Figure 5 we show the normalized neutrino likelihood maps convoluted with
the exposures of the two CR Observatories, to demonstrate the spread of the different
observed neutrino arrival directions visible from each site.
(a)
(b)
(c)
(d)
Figure 5. Neutrino likelihood maps convoluted with the exposures of the CR Observatories in
Equatorial coordinates. The two upper plots are for the high-energy cascades, while the two lower
ones are for the high-energy tracks. The declination-dependent exposure of Auger is applied in
(a) and (c) and that of TA in plots (b) and (d).
– 13 –
The test statistic T S is defined as:
T S = 2 log
L(ns )
.
L(ns = 0)
(4.4)
In accordance with Wilk’s theorem [48], the test statistic is expected to follow a
distribution close to χ2 of one degree of freedom, as ns is the only free parameter. This
assumption has been explicitly verified and is used to calculate the pre-trial p-values.
To evaluate the sensitivity and discovery potential of this method we perform the
same simulation of cosmic-ray signal events as in Section 4.1. The only difference is that
in this case the sources are sampled from each neutrino likelihood map. In Table 2 the
discovery potential and sensitivity calculations are shown in terms of the total number of
cosmic-ray signal events. We note that in these simulations we adopted the same value of
deflection parameter D in the log L as the one used to simulate the CR deflections. If the
actual deflections were different than the values of D considered in log L the discovery
potential would become worse. The comparison of the discovery potentials obtained for
this method with those obtained for the cross-correlation in the previous subsection is
non-trivial, because in the cross-correlation case they are already penalized for the trial
factor of the scan in the angular scale. On the other hand, for the likelihood method
a fixed deflection parameter D is adopted, and hence smaller required values of ns may
result with the likelihood method.
Table 2. Sensitivities and pre-trial 3σ and 5σ discovery potentials (DP(3σ) and DP(5σ)) for
the likelihood stacking method in terms of the total number of cosmic-ray signal events.
D
3◦
6◦
9◦
4.3
High-energy tracks
sensitivities DP(3σ) DP(5σ)
7.4
15.7
29.1
12.9
27.1
47.8
18.0
38.5
64.5
High-energy cascades
sensitivities DP(3σ) DP(5σ)
22.8
55.4
89.9
32.0
72.6
121.2
53.1
98.6
163.7
Results
The results of the cross-correlation method applied to the data are shown in Figures 6a
and 6b for the high-energy tracks and high-energy cascades, respectively. Here the fractional excess relative to the expectation for an isotropic CR distribution, [np (α)/hniso
p (α)i]−
1, is plotted as a function of the angular separation between the neutrino and cosmicray pairs. The dots represent the data, and the ranges corresponding to the 1σ, 2σ and
3σ confidence bands obtained in isotropic realizations of CR arrival directions are also
shown.
For the cross-correlation with the sample of neutrino tracks, the maximum departure from the expectation of an isotropic CR flux occurs at an angular distance of
1◦ (Figure 6a), where 0.38 pairs were expected on average and 2 pairs are detected.
– 14 –
2
Expected Range (3σ)
Expected Range (2σ)
Expected Range (1σ)
Tracks
4
3
Relative excess of pairs
Relative excess of pairs
5
2
1
0
(a)
-1
Expected Range (3σ)
Expected Range (2σ)
Expected Range (1σ)
Cascades
1.5
1
0.5
0
-0.5
(b)
-1
0
5
10
15
20
25
Maximum separation angle [°]
30
0
5
10
15
20
25
Maximum separation angle [°]
30
Figure 6. Relative excess of pairs, [np (α)/hniso
p (α)i] − 1, as a function of the maximum angular
separation between the neutrino and UHECR pairs, for the analysis done with the track-like
events (a) and with the cascade events (b). The 1σ, 2σ and 3σ fluctuations expected from an
isotropic distribution of arrival directions of CRs are shown in red, blue and grey, respectively.
The post-trial p-value is 28%. For the analysis done using the high-energy cascades
(Figure 6b), the smallest pre-trial p-value is obtained at an angular distance of 22◦ ,
for which 575 pairs are observed while 490.3 were expected on average. The post-trial
p-value is 5.0 × 10−4 assuming an isotropic flux of CRs arriving at the Earth.
By looking at Figure 7 one can infer that most of the excess of pairs in this case is
due to the fact that there are several high-energy cascades in regions with large densities
of UHECRs, i.e., near the Super-Galactic plane and at the TA ‘hot spot’ [38], which is
a 20◦ radius region centered at the Galactic coordinates (ℓ, b) ≃ (177◦ , 50◦ )2 .
We also perform some a posteriori tests of the cross-correlation results, considering
separately the data of Auger and TA. It was observed that both samples lead to a
minimum at 22◦ , with the TA post-trial p-value being 9.3 × 10−4 and that of Auger
being 4.1 × 10−2 . Thus, when considering the entire UHECR data set, this minimum
gets reinforced.
The results of the likelihood stacking method are summarized in Table 3. The
most significant deviation from the isotropic flux is found for the magnetic deflection
parameter D = 6◦ for the cascade sample. The observed pre-trial p-value is 2.7 × 10−4 .
Due to this rather small value the post-trial p-value calculation based on generating
background-only samples and counting the fraction of those more significant than the
result is not feasible. We then conservatively apply a trial factor of 3 to account for the
3 values of the magnetic deflection parameter D used in the analysis3 . The obtained
post-trial p-value is 8.0 × 10−4 .
2
The presence of two cascade neutrino events near this hot spot was already pointed out in Ref. [16].
This approach is conservative since when using generated background-only samples it was observed
that the significances obtained for D = 3◦ , 6◦ , and 9◦ are strongly correlated. When these simulations
were used to obtain trial factors for less significant pre-trial p-values we obtained trial factor values
smaller than 2.
3
– 15 –
Figure 7. Maps in Equatorial and Galactic coordinates showing the arrival directions of the
IceCube cascades (black dots) and tracks (diamonds), as well as those of the UHECRs detected
by the Pierre Auger Observatory (magenta stars) and Telescope Array (orange stars). The
circles around the showers indicate angular errors. The black diamonds are the HESE tracks
while the blue diamonds stand for the tracks from the through-going muon sample. The blue
curve indicates the Super-Galactic plane.
It is important to stress that all the p-values quoted for both analyses above are with
respect to the null hypothesis of an isotropic UHECR flux, as analyses of the distributions
of their arrival directions yielded no evidence of anisotropy at discovery level. However,
directions with higher densities of UHECRs, such as the TA ‘hot spot’ [38] and the
direction of Cen A [9], have been reported. Hence, as an additional a posteriori study
for both analyses, we have also evaluated the significance under the hypothesis of an
isotropic distribution of neutrinos. In this case, the UHECR positions have been kept
– 16 –
D
3◦
6◦
9◦
ns
4.2
0.5
0
High-energy tracks
TS
pre-trial p-value
0.6
0.22
−3
2.7 × 10
0.48
0
under-fluctuation
High-energy cascades
ns
TS
pre-trial p-value
53.7
8.21
2.1 × 10−3
85.7
11.99 2.7 × 10−4
106.1 11.32 3.8 × 10−4
Table 3. Results for the likelihood stacking analyses with the high-energy tracks and high-energy
cascades.
fixed, thus preserving the degree of anisotropy in the arrival directions of CRs. The
arrival directions of neutrinos have been simulated producing random right ascensions,
while keeping their declination fixed and thus accounting for the declination dependence
in the IceCube acceptance. This random-neutrino test assesses the extent to which
the p-values previously obtained for the clustering of cosmic rays around the neutrino
directions could be affected by chance alignments of the neutrinos with known clustering
in the cosmic-ray sky.
For the cross-correlation analysis the post-trial p-value obtained under the hypothesis of an isotropic distribution of neutrinos is 8.5 × 10−3 . A similar post-trial p-value
can be calculated for the likelihood stacking analysis by applying the analysis for all
three angular deflection hypothesis D = 3◦ , 6◦ , and 9◦ and selecting the most significant result. This can then be compared to the significance obtained for real data and it
was found that in four cases out of 3000 the significance of the generated samples was
higher. Thus, for the likelihood stacking analysis the post-trial p-value with respect to
the isotropic neutrino flux hypothesis is 1.3 × 10−3 (i.e., of about 3σ). We see that for
both the cross-correlation and the likelihood stacking analyses, the p-values obtained
under the null hypothesis of isotropic neutrinos turn out to be larger than the ones obtained under the null hypothesis of isotropic CRs, the differences reflecting the extent
to which the original p-values, from the isotropic cosmic-ray hypothesis, are due to an
accidental alignment of the neutrinos with the known clustering of the cosmic rays.
An a posteriori scan over the values of the assumed deflection D for the stacking
analysis with cascades, shown in Figure 8, reveals that the minimum p-value happens
very close to one of the values adopted for the analysis, i.e., D = 6◦ .
The angular distance at which an excess would occur in the case of the crosscorrelation includes not only the magnetic deflections at the corresponding CR energies
but also the experimental angular uncertainties. In the case of cascades, the angular
uncertainty is ∼ 15◦ and it is ∼ 1◦ for the CRs. Since most CRs in the data set have
ECR ∼ 60 EeV, the assumed magnetic deflection, where the smallest p-value is found in
the case of the likelihood analysis with the cascades (σMD (ECR ) = 6◦ × 100 EeV/ECR ),
is ∼ 10◦ in most cases. To translate this into an angular scale where one would find
an excess in the cross-correlation analysisp
(if there were a signal), we add the different
(15◦ )2 + (1◦ )2 + (10◦ )2 ≈ 18◦ . This scale
angular scales in quadrature, obtaining
is comparable to the 22◦ where the smallest p-value is found for the cross-correlation
performed with the cascades. Hence, the magnetic deflection of the CRs one would infer
– 17 –
pre-trial p-value
10-2
Cascades
10-3
10-4
2
3
4
5
6
D [°]
7
8
9
10
Figure 8. A posteriori angular scan for the stacking with the high-energy cascades. The analysis
was done only for the three chosen values of D: 3◦ , 6◦ and 9◦ .
from the cross-correlation analysis with the cascades is comparable to the value leading
to the smallest p-value in the likelihood analysis, even if none of the results are at a level
where any strong claims can be made.
The consistent and significant correlation of UHECRs with the high-energy cascades observed in both the cross-correlation and stacking analyses forms a potentially
interesting result, which we will continue to monitor in the future.
5
5.1
Stacking search with the 4 year point-source sample
Method and discovery potential
This analysis looks for excesses in the neutrino point-source data set, consisting of
through-going tracks and described in Section 2.1.3, around the directions of the highestenergy UHECRs. We use a likelihood method which is a generalization of the one described in Section 4.2 [24, 49], but now the measured positions of the UHECRs are
stacked as sources.
The log of the likelihood function is defined as:
log L(ns , γ) =
Nν
X
i=1
log
ns
ns tot
S + 1−
Bi ,
Nν i
Nν
(5.1)
where ns is the number of signal events in the sample and γ is the spectral index of
the neutrino source candidates, assumed to collectively follow an unbroken power-law
spectrum ∝ E −γ . Nν is the total number of astrophysical neutrino candidate events in
the sample. Sitot is the signal PDF for the stacked sources and Bi is the background
PDF.
Signal events from an astrophysical source j are expected to be clustered around
the direction of the source ~rj according to the Gaussian distribution:
– 18 –
Gji
|~ri − ~rj |2
1
exp
−
=
2
2
2πσij
2σij
!
,
(5.2)
q
2 (E ) accounts for the spread due to the angular resolution
where σij = σi2 + σj2 + σMD
j
of the IceCube event i, that of the CR event j, as well as for the spread due to the
assumed magnetic deflection of the CR with energy Ej .
The signal PDF Sij also accounts for the energy- (and declination-) dependent
response of the IceCube detector, P (δi , Ei |γ), which can be obtained from Monte Carlo
simulations of events produced by a source with a power-law spectrum of index γ. The
single-source signal PDF is then
S(~ri , r~j , Ei , γ) = Gji × P (δi , Ei |γ).
(5.3)
The total PDF obtained after stacking the NCR UHECR directions is given by
Sitot
=
NP
CR
RIC (δj , γ)S(~ri , ~rj , Ei , γ)
j=1
NP
CR
,
(5.4)
RIC (δj , γ)
j=1
where RIC (δj , γ) is the detector acceptance of IceCube at declination δj for a source of
spectral index γ.
Events which are atmospheric muons and/or neutrinos are expected to be distributed uniformly within each declination band. The distribution of the values of the
energy estimator E of these events can be indicated by P (δi , E|φatm ). The background
probability distribution can then be expressed as
B(~ri , Ei ) = B(δi ) × P (δi , Ei |φatm ),
(5.5)
where B(δi ) is the declination dependence of the sample.
The number of signal events ns and the spectral index of the sources γ are unknown,
but the best estimates of these two parameters, n̂s and γ̂, can be obtained as those
maximizing the likelihood. The test statistic is then obtained as
T S = 2 log
L(n̂s , γ̂)
.
L(ns = 0)
(5.6)
The significance of an observation can then be estimated by repeating the process on
datasets randomized in right ascension and computing the fraction of randomized samples that produce a value of the T S bigger than that observed in the data.
The performance of this kind of search can be quantified by the median source flux
required for 5σ discovery, defined similarly to that in Section 4.2 but in terms of the
astrophysical neutrino flux. This is calculated by repeating the test on datasets with ns
additional simulated signal events injected in the direction of the sources.
– 19 –
Since using all of the 318 events described in Section 2 as sources with their associated angular extensions would essentially cover the whole sky, the possible gain
associated to the stacking of more sources is reduced. Restricting the UHECR sample
to those with energies above a given threshold Eth could give the advantage of having
smaller associated magnetic spreads, potentially enhancing the discovery potential. We
look for an optimum value of Eth for which the per-source flux required for discovery
can be minimized as a consequence of these two competing effects.
-10
10
-2 -1
E dN/dE [TeV cm s ]
5σ DP flux per source
North, D=3°
South, D=3°
All, D=3°
North, D=6°
South, D=6°
All, D=6°
-11
2
10
-12
10
60
70
80
90
100
Eth [EeV]
110
120
130
Figure 9. Pre-trial discovery potential at the 5σ level. The normalization of the flux per source
required is shown as a function of the UHECR threshold energy Eth . The results from Northern
and Southern skies, as well as the whole sky, are shown for D = 3◦ and 6◦ .
A simulation was then performed to determine the discovery potential of the UHECR
stacking analysis obtained for different values of Eth (see Figure 9) for both the Southern
and Northern hemispheres separately as well as for the whole sky sample. To calculate
the discovery potentials, events were injected from point sources in the direction of the
UHECRs, adopting source spectra with γ = 2 and considering two deflection hypotheses,
D = 3◦ and 6◦ . Each point source was positioned with a deflection ∆j from
q the UHECR,
2 (E ).
where ∆j is sampled randomly from a Gaussian distribution of width σj2 + σMD
j
As seen in Figure 9, the discovery potentials are characterized by a broad flat region,
based on which a value of Eth = 85 EeV was chosen. This keeps the 12 highest-energy
UHECRs in the Southern sky and 15 in the Northern sky.
Due to the different energy ranges between the neutrino candidate events in the
Southern hemisphere (∼100 TeV - 100 PeV) and in the Northern hemisphere (∼1 TeV
- 1 PeV), the flux normalization required for Northern sources turns out to be smaller
than for Southern ones. However, thanks to the gain provided by having more stacked
– 20 –
sources, the whole sky sensitivity turns out to be similar to the one in the Northern sky
alone (Figure 9). We have thus considered just the whole sky sample with Eth = 85 EeV
in this analysis.
5.2
Results
Applying this analysis to the data, all observations were found to be compatible with
the background hypothesis. For the deflection hypothesis of D = 3◦ , the p-value was
found to be 17.3% with a fitted excess of ns ∼ 123 events and a fitted source spectrum of
E −3.24 , while the p-value was found to be > 50% for the D = 6◦ hypothesis. Accounting
for the trial factor due to having tested both the D = 3◦ and the D = 6◦ hypotheses,
the post-trial p-value was found to be 25.4%.
6
Conclusions
Three analyses have been performed to investigate correlations between the 318 UHECRs
measured by the Auger Observatory and the Telescope Array with various samples of
IceCube neutrino events, and the results obtained are all below 3.3σ.
The smallest post-trial p-values were obtained when considering IceCube highenergy cascades. In the case of the cross-correlation analysis, the minimum was found for
an angular scale of 22◦ , with a post-trial p-value of 5.0×10−4 under the assumption of an
isotropic flux of UHECRs and 8.5 × 10−3 in the a posteriori study under the assumption
of an isotropic flux of neutrinos. For the stacking done with the high-energy cascades and
a deflection hypothesis of D = 6◦ , a post-trial p-value of 8.0 × 10−4 was obtained under
the assumption of an isotropic flux of UHECRs and 1.3 × 10−3 under the a posteriori
assumption of an isotropic flux of neutrinos. The two results correspond to comparable
magnetic deflections of CRs. These correlation excesses arise mostly from pairs of events
in the region of the TA hot spot and also in regions close to the Super-Galactic plane
where some excess of events is seen in the Auger sample, but at present the results
are not significant enough to draw any strong conclusions and are also compatible with
being fluctuations of an isotropic distribution. It will be interesting to further study
these findings with increased statistics in the future. On the other hand, the p-values
obtained in the studies involving neutrino tracks are large, being totally compatible
with the absence of correlations between the arrival directions of the neutrino tracks
and the UHECRs. Similarly, the p-values obtained from the stacking analyses with the
point-source sample and the 27 highest-energy UHECRs show no significant excess of
neutrinos in the directions of these UHECRs.
We note that the absence of strong correlations between neutrinos and UHECRs
may have different causes. In particular, one has to keep in mind that if the strong
suppression in the cosmic-ray flux observed above 40–50 EeV is due to the attenuation
of protons in the CMB through photopion production (or of nuclei due to photodisintegrations), the majority of the observed UHECRs above 50 EeV should have been
produced in sources relatively nearby, i.e., within ∼ 200 Mpc. On the other hand, the
astrophysical neutrinos may come from sources at any distance since neutrinos are not
– 21 –
limited by absorption. Hence, only a small fraction of the extragalactic neutrinos, those
from sources relatively nearby, may have the same sources as the observed UHECRs.
Considering for instance that the neutrino sources extend to at least z=1, the overall
extragalactic contribution arising from sources closer than 200 Mpc is not expected to
exceed a few percent (in the case of no source evolution and uniform source distribution)
and could be particularly suppressed if the evolution of the sources is strong. Another
difficulty in observing common UHECR and neutrino sources is that while the neutrinos
arrive straight from their sources, the deflections of charged cosmic rays in Galactic and
extragalactic magnetic fields induce sizeable delays between the arrival times of CRs and
those of the neutrinos, which are typically much larger than the duration of the experiments. Hence, if the sources are burst-like rather than steady, the burst of neutrinos
would arrive long before the associated UHECRs and their simultaneous observation
could not be feasible. Finally, the sources capable of producing PeV neutrinos, which
are those able to accelerate protons up to energies of a few tens of PeV, may only rarely
be able to also accelerate cosmic rays to ultrahigh-energies. Hence, it may be natural to
expect that only a small fraction of the observed energetic neutrinos come from sources
that also produce UHECRs.
In conclusion, further insight will potentially arise from increased statistics and
eventually with the inclusion of CR composition information that may become available
so as to better model possible effects of magnetic field deflections. This may help to
understand if there is a contribution in the astrophysical neutrino signal observed by
IceCube correlated to the sources of the observed UHECR.
Acknowledgments
The IceCube Collaboration acknowledges the support from the following agencies: U.S.
National Science Foundation-Office of Polar Programs, U.S. National Science FoundationPhysics Division, University of Wisconsin Alumni Research Foundation, the Grid Laboratory Of Wisconsin (GLOW) grid infrastructure at the University of Wisconsin - Madison, the Open Science Grid (OSG) grid infrastructure; U.S. Department of Energy, and
National Energy Research Scientific Computing Center, the Louisiana Optical Network
Initiative (LONI) grid computing resources; Natural Sciences and Engineering Research
Council of Canada, WestGrid and Compute/Calcul Canada; Swedish Research Council, Swedish Polar Research Secretariat, Swedish National Infrastructure for Computing
(SNIC), and Knut and Alice Wallenberg Foundation, Sweden; German Ministry for Education and Research (BMBF), Deutsche Forschungsgemeinschaft (DFG), Helmholtz Alliance for Astroparticle Physics (HAP), Research Department of Plasmas with Complex
Interactions (Bochum), Germany; Fund for Scientific Research (FNRS-FWO), FWO
Odysseus programme, Flanders Institute to encourage scientific and technological research in industry (IWT), Belgian Federal Science Policy Office (Belspo); University of
Oxford, United Kingdom; Marsden Fund, New Zealand; Australian Research Council;
Japan Society for Promotion of Science (JSPS); the Swiss National Science Foundation
(SNSF), Switzerland; National Research Foundation of Korea (NRF); Danish National
Research Foundation, Denmark (DNRF).
– 22 –
The successful installation, commissioning, and operation of the Pierre Auger Observatory would not have been possible without the strong commitment and effort from the
technical and administrative staff in Malargüe. We are very grateful to the following
agencies and organizations for financial support:
Comisión Nacional de Energı́a Atómica, Agencia Nacional de Promoción Cientı́fica
y Tecnológica (ANPCyT), Consejo Nacional de Investigaciones Cientı́ficas y Técnicas
(CONICET), Gobierno de la Provincia de Mendoza, Municipalidad de Malargüe, NDM
Holdings and Valle Las Leñas, in gratitude for their continuing cooperation over
land access, Argentina; the Australian Research Council; Conselho Nacional de Desenvolvimento Cientı́fico e Tecnológico (CNPq), Financiadora de Estudos e Projetos
(FINEP), Fundação de Amparo à Pesquisa do Estado de Rio de Janeiro (FAPERJ), São
Paulo Research Foundation (FAPESP) Grants No. 2010/07359-6 and No. 1999/054043, Ministério de Ciência e Tecnologia (MCT), Brazil; Grant No. MSMT-CR LG13007,
No. 7AMB14AR005, and the Czech Science Foundation Grant No. 14-17501S, Czech
Republic; Centre de Calcul IN2P3/CNRS, Centre National de la Recherche Scientifique (CNRS), Conseil Régional Ile-de-France, Département Physique Nucléaire
et Corpusculaire (PNC-IN2P3/CNRS), Département Sciences de l’Univers (SDUINSU/CNRS), Institut Lagrange de Paris (ILP) Grant No. LABEX ANR-10-LABX63, within the Investissements d’Avenir Programme Grant No. ANR-11-IDEX-0004-02,
France; Bundesministerium für Bildung und Forschung (BMBF), Deutsche Forschungsgemeinschaft (DFG), Finanzministerium Baden-Württemberg, Helmholtz Alliance for
Astroparticle Physics (HAP), Helmholtz-Gemeinschaft Deutscher Forschungszentren
(HGF), Ministerium für Wissenschaft und Forschung, Nordrhein Westfalen, Ministerium für Wissenschaft, Forschung und Kunst, Baden-Württemberg, Germany; Istituto Nazionale di Fisica Nucleare (INFN), Istituto Nazionale di Astrofisica (INAF),
Ministero dell’Istruzione, dell’Universitá e della Ricerca (MIUR), Gran Sasso Center for
Astroparticle Physics (CFA), CETEMPS Center of Excellence, Ministero degli Affari
Esteri (MAE), Italy; Consejo Nacional de Ciencia y Tecnologı́a (CONACYT), Mexico;
Ministerie van Onderwijs, Cultuur en Wetenschap, Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Stichting voor Fundamenteel Onderzoek der Materie
(FOM), Netherlands; National Centre for Research and Development, Grants No. ERANET-ASPERA/01/11 and No. ERA-NET-ASPERA/02/11, National Science Centre,
Grants No. 2013/08/M/ST9/00322, No. 2013/08/M/ST9/00728 and No. HARMONIA
5 - 2013/10/M/ST9/00062, Poland; Portuguese national funds and FEDER funds within
Programa Operacional Factores de Competitividade through Fundação para a Ciência
e a Tecnologia (COMPETE), Portugal; Romanian Authority for Scientific Research
ANCS, CNDI-UEFISCDI partnership projects Grants No. 20/2012 and No. 194/2012,
Grants No. 1/ASPERA2/2012 ERA-NET, No. PN-II-RU-PD-2011-3-0145-17 and No.
PN-II-RU-PD-2011-3-0062, the Minister of National Education, Programme Space Technology and Advanced Research (STAR), Grant No. 83/2013, Romania; Slovenian Research Agency, Slovenia; Comunidad de Madrid, FEDER funds, Ministerio de Educación
y Ciencia, Xunta de Galicia, European Community 7th Framework Program, Grant
No. FP7-PEOPLE-2012-IEF-328826, Spain; Science and Technology Facilities Council,
– 23 –
United Kingdom; Department of Energy, Contracts No. DE-AC02-07CH11359, No. DEFR02-04ER41300, No. DE-FG02-99ER41107 and No. DE-SC0011689, National Science
Foundation, Grant No. 0450696, The Grainger Foundation, USA; NAFOSTED, Vietnam; Marie Curie-IRSES/EPLANET, European Particle Physics Latin American Network, European Union 7th Framework Program, Grant No. PIRSES-2009-GA-246806
and PIOF-GA-2013-624803; and UNESCO.
The Telescope Array experiment is supported by the Japan Society for the Promotion of
Science through Grants-in-Aid for Scientific Research on Specially Promoted Research
(21000002) “Extreme Phenomena in the Universe Explored by Highest Energy Cosmic
Rays” and for Scientific Research (19104006), and the Inter-University Research Program of the Institute for Cosmic Ray Research; by the U.S. National Science Foundation awards PHY-0307098, PHY-0601915, PHY-0649681, PHY-0703893, PHY-0758342,
PHY-0848320, PHY-1069280, PHY-1069286, PHY-1404495 and PHY-1404502; by the
National Research Foundation of Korea (2007-0093860, R32-10130, 2012R1A1A2008381,
2013004883); by the Russian Academy of Sciences, RFBR grants 11-02-01528a and 1302-01311a (INR), IISN project No. 4.4502.13, and Belgian Science Policy under IUAP
VII/37 (ULB). The foundations of Dr. Ezekiel R. and Edna Wattis Dumke, Willard L.
Eccles, and George S. and Dolores Doré Eccles all helped with generous donations. The
State of Utah supported the project through its Economic Development Board, and the
University of Utah through the Office of the Vice President for Research. The experimental site became available through the cooperation of the Utah School and Institutional
Trust Lands Administration (SITLA), U.S. Bureau of Land Management, and the U.S.
Air Force. We also wish to thank the people and the officials of Millard County, Utah for
their steadfast and warm support. We gratefully acknowledge the contributions from the
technical staffs of our home institutions. An allocation of computer time from the Center
for High Performance Computing at the University of Utah is gratefully acknowledged.
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– 26 –
A
Neutrino
– 27 –
The IceCube Collaboration
M. G. Aartsen2 , K. Abraham32 , M. Ackermann48 , J. Adams15 , J. A. Aguilar12 ,
M. Ahlers29 , M. Ahrens39 , D. Altmann23 , T. Anderson45 , I. Ansseau12 , M. Archinger30 ,
C. Arguelles29 , T. C. Arlen45 , J. Auffenberg1 , X. Bai37 , S. W. Barwick26 , V. Baum30 ,
R. Bay7 , J. J. Beatty17, 18 , J. Becker Tjus10 , K.-H. Becker47 , E. Beiser29 , P. Berghaus48 ,
D. Berley16 , E. Bernardini48 , A. Bernhard32 , D. Z. Besson27 , G. Binder8, 7 , D. Bindig47 ,
M. Bissok1 , E. Blaufuss16 , J. Blumenthal1 , D. J. Boersma46 , C. Bohm39 , M. Börner20 ,
F. Bos10 , D. Bose41 , S. Böser30 , O. Botner46 , J. Braun29 , L. Brayeur13 , H.-P. Bretz48 ,
N. Buzinsky22 , J. Casey5 , M. Casier13 , E. Cheung16 , D. Chirkin29 , A. Christov24 ,
K. Clark42 , L. Classen23 , S. Coenders32 , D. F. Cowen45, 44 , A. H. Cruz Silva48 ,
J. Daughhetee5 , J. C. Davis17 , M. Day29 , J. P. A. M. de André21 , C. De Clercq13 ,
E. del Pino Rosendo30 , H. Dembinski33 , S. De Ridder25 , P. Desiati29 , K. D. de Vries13 ,
G. de Wasseige13 , M. de With9 , T. DeYoung21 , J. C. Dı́az-Vélez29 , V. di Lorenzo30 ,
J. P. Dumm39 , M. Dunkman45 , B. Eberhardt30 , T. Ehrhardt30 , B. Eichmann10 ,
S. Euler46 , P. A. Evenson33 , S. Fahey29 , A. R. Fazely6 , J. Feintzeig29 , J. Felde16 ,
K. Filimonov7 , C. Finley39 , T. Fischer-Wasels47 , S. Flis39 , C.-C. Fösig30 , T. Fuchs20 ,
T. K. Gaisser33 , R. Gaior14 , J. Gallagher28 , L. Gerhardt8, 7 , K. Ghorbani29 , D. Gier1 ,
L. Gladstone29 , M. Glagla1 , T. Glüsenkamp48 , A. Goldschmidt8 , G. Golup13 ,
J. G. Gonzalez33 , D. Góra48 , D. Grant22 , Z. Griffith29 , A. Groß32 , C. Ha8, 7 ,
C. Haack1 , A. Haj Ismail25 , A. Hallgren46 , F. Halzen29 , E. Hansen19 , B. Hansmann1 ,
K. Hanson29 , D. Hebecker9 , D. Heereman12 , K. Helbing47 , R. Hellauer16 , S. Hickford47 ,
J. Hignight21 , G. C. Hill2 , K. D. Hoffman16 , R. Hoffmann47 , K. Holzapfel32 ,
A. Homeier11 , K. Hoshina29, a , F. Huang45 , M. Huber32 , W. Huelsnitz16 , P. O. Hulth39 ,
K. Hultqvist39 , S. In41 , A. Ishihara14 , E. Jacobi48 , G. S. Japaridze4 , M. Jeong41 ,
K. Jero29 , M. Jurkovic32 , A. Kappes23 , T. Karg48 , A. Karle29 , M. Kauer29, 34 ,
A. Keivani45 , J. L. Kelley29 , J. Kemp1 , A. Kheirandish29 , J. Kiryluk40 , J. Kläs47 ,
S. R. Klein8, 7 , G. Kohnen31 , R. Koirala33 , H. Kolanoski9 , R. Konietz1 , L. Köpke30 ,
C. Kopper22 , S. Kopper47 , D. J. Koskinen19 , M. Kowalski9, 48 , K. Krings32 , G. Kroll30 ,
M. Kroll10 , G. Krückl30 , J. Kunnen13 , N. Kurahashi36 , T. Kuwabara14 , M. Labare25 ,
J. L. Lanfranchi45 , M. J. Larson19 , M. Lesiak-Bzdak40 , M. Leuermann1 , J. Leuner1 ,
L. Lu14 , J. Lünemann13 , J. Madsen38 , G. Maggi13 , K. B. M. Mahn21 , M. Mandelartz10 ,
R. Maruyama34 , K. Mase14 , H. S. Matis8 , R. Maunu16 , F. McNally29 , K. Meagher12 ,
M. Medici19 , A. Meli25 , T. Menne20 , G. Merino29 , T. Meures12 , S. Miarecki8, 7 ,
E. Middell48 , L. Mohrmann48 , T. Montaruli24 , R. Morse29 , R. Nahnhauer48 ,
U. Naumann47 , G. Neer21 , H. Niederhausen40 , S. C. Nowicki22 , D. R. Nygren8 ,
A. Obertacke Pollmann47 , A. Olivas16 , A. Omairat47 , A. O’Murchadha12 ,
T. Palczewski43 , H. Pandya33 , D. V. Pankova45 , L. Paul1 , J. A. Pepper43 ,
C. Pérez de los Heros46 , C. Pfendner17 , D. Pieloth20 , E. Pinat12 , J. Posselt47 ,
P. B. Price7 , G. T. Przybylski8 , M. Quinnan45 , C. Raab12 , L. Rädel1 , M. Rameez24 ,
K. Rawlins3 , R. Reimann1 , M. Relich14 , E. Resconi32 , W. Rhode20 , M. Richman36 ,
S. Richter29 , B. Riedel22 , S. Robertson2 , M. Rongen1 , C. Rott41 , T. Ruhe20 ,
D. Ryckbosch25 , L. Sabbatini29 , H.-G. Sander30 , A. Sandrock20 , J. Sandroos30 ,
S. Sarkar19, 35 , K. Schatto30 , M. Schimp1 , T. Schmidt16 , S. Schoenen1 , S. Schöneberg10 ,
– 28 –
A. Schönwald48 , L. Schulte11 , L. Schumacher1 , D. Seckel33 , S. Seunarine38 , D. Soldin47 ,
M. Song16 , G. M. Spiczak38 , C. Spiering48 , M. Stahlberg1 , M. Stamatikos17, b ,
T. Stanev33 , A. Stasik48 , A. Steuer30 , T. Stezelberger8 , R. G. Stokstad8 , A. Stößl48 ,
R. Ström46 , N. L. Strotjohann48 , G. W. Sullivan16 , M. Sutherland17 , H. Taavola46 ,
I. Taboada5 , J. Tatar8, 7 , S. Ter-Antonyan6 , A. Terliuk48 , G. Tešić45 , S. Tilav33 ,
P. A. Toale43 , M. N. Tobin29 , S. Toscano13 , D. Tosi29 , M. Tselengidou23 , A. Turcati32 ,
E. Unger46 , M. Usner48 , S. Vallecorsa24 , J. Vandenbroucke29 , N. van Eijndhoven13 ,
S. Vanheule25 , J. van Santen48 , J. Veenkamp32 , M. Vehring1 , M. Voge11 , M. Vraeghe25 ,
C. Walck39 , A. Wallace2 , M. Wallraff1 , N. Wandkowsky29 , Ch. Weaver22 , C. Wendt29 ,
S. Westerhoff29 , B. J. Whelan2 , K. Wiebe30 , C. H. Wiebusch1 , L. Wille29 ,
D. R. Williams43 , H. Wissing16 , M. Wolf39 , T. R. Wood22 , K. Woschnagg7 , D. L. Xu29 ,
X. W. Xu6 , Y. Xu40 , J. P. Yanez48 , G. Yodh26 , S. Yoshida14 , M. Zoll39
1 III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
2 Department of Physics, University of Adelaide, Adelaide, 5005, Australia
3 Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence
Dr., Anchorage, AK 99508, USA
4 CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA
5 School of Physics and Center for Relativistic Astrophysics, Georgia Institute of
Technology, Atlanta, GA 30332, USA
6 Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA
7 Dept. of Physics, University of California, Berkeley, CA 94720, USA
8 Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
9 Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany
10 Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum,
Germany
11 Physikalisches Institut, Universität Bonn, Nussallee 12, D-53115 Bonn, Germany
12 Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
13 Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgium
14 Dept. of Physics, Chiba University, Chiba 263-8522, Japan
15 Dept. of Physics and Astronomy, University of Canterbury, Private Bag 4800,
Christchurch, New Zealand
16 Dept. of Physics, University of Maryland, College Park, MD 20742, USA
17 Dept. of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State
University, Columbus, OH 43210, USA
18 Dept. of Astronomy, Ohio State University, Columbus, OH 43210, USA
19 Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
20 Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany
21 Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI 48824,
USA
22 Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1
23 Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität ErlangenNürnberg, D-91058 Erlangen, Germany
24 Département de physique nucléaire et corpusculaire, Université de Genève, CH-1211
– 29 –
Genève, Switzerland
25 Dept. of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium
26 Dept. of Physics and Astronomy, University of California, Irvine, CA 92697, USA
27 Dept. of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA
28 Dept. of Astronomy, University of Wisconsin, Madison, WI 53706, USA
29 Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin, Madison, WI 53706, USA
30 Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz,
Germany
31 Université de Mons, 7000 Mons, Belgium
32 Technische Universität München, D-85748 Garching, Germany
33 Bartol Research Institute and Dept. of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA
34 Dept. of Physics, Yale University, New Haven, CT 06520, USA
35 Dept. of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
36 Dept. of Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104,
USA
37 Physics Department, South Dakota School of Mines and Technology, Rapid City, SD
57701, USA
38 Dept. of Physics, University of Wisconsin, River Falls, WI 54022, USA
39 Oskar Klein Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm,
Sweden
40 Dept. of Physics and Astronomy, Stony Brook University, Stony Brook, NY 117943800, USA
41 Dept. of Physics, Sungkyunkwan University, Suwon 440-746, Korea
42 Dept. of Physics, University of Toronto, Toronto, Ontario, Canada, M5S 1A7
43 Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA
44 Dept. of Astronomy and Astrophysics, Pennsylvania State University, University
Park, PA 16802, USA
45 Dept. of Physics, Pennsylvania State University, University Park, PA 16802, USA
46 Dept. of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala,
Sweden
47 Dept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
48 DESY, D-15735 Zeuthen, Germany
a Earthquake Research Institute, University of Tokyo, Bunkyo, Tokyo 113-0032, Japan
b NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
– 30 –
The Pierre Auger Collaboration
A. Aab40 , P. Abreu71 , M. Aglietta50,49 , E.J. Ahn86 , I. Al Samarai30 ,
I.F.M. Albuquerque16 , I. Allekotte1 , P. Allison91 , A. Almela11,8 , J. Alvarez
Castillo64 , J. Alvarez-Muñiz81 , R. Alves Batista39 , M. Ambrosio47 , A. Aminaei65 ,
L. Anchordoqui85 , B. Andrada8 , S. Andringa71 , C. Aramo47 , F. Arqueros78 , N. Arsene74 ,
H. Asorey1,24 , P. Assis71 , J. Aublin30 , G. Avila10 , N. Awal89 , A.M. Badescu75 , C. Baus35 ,
J.J. Beatty91 , K.H. Becker34 , J.A. Bellido12 , C. Berat31 , M.E. Bertaina51,49 , X. Bertou1 ,
P.L. Biermannb , P. Billoir30 , S.G. Blaess12 , A. Blanco71 , M. Blanco30 , J. Blazek25 ,
C. Bleve53,45 , H. Blümer35,36 , M. Boháčová25 , D. Boncioli42 , C. Bonifazi22 , N. Borodai69 ,
A.M. Botti8 , J. Brack84 , I. Brancus72 , T. Bretz38 , A. Bridgeman36 , F.L. Briechle38 ,
P. Buchholz40 , A. Bueno80 , S. Buitink65 , M. Buscemi55,43 , K.S. Caballero-Mora62 ,
B. Caccianiga46 , L. Caccianiga30 , M. Candusso48 , L. Caramete73 , R. Caruso55,43 ,
A. Castellina50,49 , G. Cataldi45 , L. Cazon71 , R. Cester51,49 , A.G. Chavez63 ,
A. Chiavassa51,49 , J.A. Chinellato17 , J.C. Chirinos Diaz88 , J. Chudoba25 , R.W. Clay12 ,
R. Colalillo57,47 , A. Coleman92 , L. Collica49 , M.R. Coluccia53,45 , R. Conceição71 ,
F. Contreras9 , M.J. Cooper12 , A. Cordier29 , S. Coutu92 , C.E. Covault82 , R. Dallier33,32 ,
S. D’Amico52,45 , B. Daniel17 , S. Dasso5,3 , K. Daumiller36 , B.R. Dawson12 ,
R.M. de Almeida23 , S.J. de Jong65,67 , G. De Mauro65 , J.R.T. de Mello Neto22 ,
I. De Mitri53,45 , J. de Oliveira23 , V. de Souza15 , J. Debatin36 , L. del Peral79 ,
O. Deligny28 , N. Dhital88 , C. Di Giulio58,48 , A. Di Matteo54,44 , M.L. Dı́az Castro17 ,
F. Diogo71 , C. Dobrigkeit17 , W. Docters66 , J.C. D’Olivo64 , A. Dorofeev84 , R.C. dos
Anjos15,d , M.T. Dova4 , A. Dundovic39 , J. Ebr25 , R. Engel36 , M. Erdmann38 ,
M. Erfani40 , C.O. Escobar86,17 , J. Espadanal71 , A. Etchegoyen8,11 , H. Falcke65,68,67 ,
K. Fang93 , G. Farrar89 , A.C. Fauth17 , N. Fazzini86 , A.P. Ferguson82 , B. Fick88 ,
J.M. Figueira8 , A. Filevich8 , A. Filipčič76,77 , O. Fratu75 , M.M. Freire6 , T. Fujii93 ,
A. Fuster8,11 , F. Gallo8,11 , B. Garcı́a7 , D. Garcia-Gamez29 , D. Garcia-Pinto78 ,
F. Gate33 , H. Gemmeke37 , A. Gherghel-Lascu72 , P.L. Ghia30 , U. Giaccari22 ,
M. Giammarchi46 , M. Giller70 , D. Glas70 , C. Glaser38 , H. Glass86 , G. Golup1 ,
M. Gómez Berisso1 , P.F. Gómez Vitale10 , N. González8 , B. Gookin84 , J. Gordon91 ,
A. Gorgi50,49 , P. Gorham94 , P. Gouffon16 , N. Griffith91 , A.F. Grillo42 , T.D. Grubb12 ,
F. Guarino57,47 , G.P. Guedes18 , M.R. Hampel8 , P. Hansen4 , D. Harari1 , T.A. Harrison12 ,
J.L. Harton84 , Q. Hasankiadeh36 , A. Haungs36 , T. Hebbeker38 , D. Heck36 , P. Heimann40 ,
A.E. Herve35 , G.C. Hill12 , C. Hojvat86 , N. Hollon93 , E. Holt36 , P. Homola69 ,
J.R. Hörandel65,67 , P. Horvath26 , M. Hrabovský26 , T. Huege36 , A. Insolia55,43 ,
P.G. Isar73 , I. Jandt34 , S. Jansen65,67 , C. Jarne4 , J.A. Johnsen83 , M. Josebachuili8 ,
A. Kääpä34 , O. Kambeitz35 , K.H. Kampert34 , P. Kasper86 , I. Katkov35 , B. Keilhauer36 ,
E. Kemp17 , R.M. Kieckhafer88 , H.O. Klages36 , M. Kleifges37 , J. Kleinfeller9 , R. Krause38 ,
N. Krohm34 , D. Kuempel38 , G. Kukec Mezek77 , N. Kunka37 , A. Kuotb Awad36 ,
D. LaHurd82 , L. Latronico49 , R. Lauer96 , M. Lauscher38 , P. Lautridou33 , D. Lebrun31 ,
P. Lebrun86 , M.A. Leigui de Oliveira21 , A. Letessier-Selvon30 , I. Lhenry-Yvon28 ,
K. Link35 , L. Lopes71 , R. López59 , A. López Casado81 , A. Lucero8 , M. Malacari12 ,
M. Mallamaci56,46 , D. Mandat25 , P. Mantsch86 , A.G. Mariazzi4 , V. Marin33 ,
I.C. Mariş80 , G. Marsella53,45 , D. Martello53,45 , H. Martinez60 , O. Martı́nez Bravo59 ,
– 31 –
J.J. Ması́as Meza3 , H.J. Mathes36 , S. Mathys34 , J. Matthews87 , J.A.J. Matthews96 ,
G. Matthiae58,48 , D. Maurizio13 , E. Mayotte83 , P.O. Mazur86 , C. Medina83 , G. MedinaTanco64 , V.B.B. Mello22 , D. Melo8 , A. Menshikov37 , S. Messina66 , M.I. Micheletti6 ,
L. Middendorf38 , I.A. Minaya78 , L. Miramonti56,46 , B. Mitrica72 , L. Molina-Bueno80 ,
S. Mollerach1 , F. Montanet31 , C. Morello50,49 , M. Mostafá92 , C.A. Moura21 , G. Müller38 ,
M.A. Muller17,20 , S. Müller36 , I. Naranjo1 , S. Navas80 , P. Necesal25 , L. Nellen64 ,
A. Nelles65,67 , J. Neuser34 , P.H. Nguyen12 , M. Niculescu-Oglinzanu72 , M. Niechciol40 ,
L. Niemietz34 , T. Niggemann38 , D. Nitz88 , D. Nosek27 , V. Novotny27 , H. Nožka26 ,
L.A. Núñez24 , L. Ochilo40 , F. Oikonomou92 , A. Olinto93 , N. Pacheco79 , D. Pakk
Selmi-Dei17 , M. Palatka25 , J. Pallotta2 , P. Papenbreer34 , G. Parente81 , A. Parra59 ,
T. Paul90,85 , M. Pech25 , J. Pȩkala69 , R. Pelayo61 , J. Peña-Rodriguez24 , I.M. Pepe19 ,
L. Perrone53,45 , E. Petermann95 , C. Peters38 , S. Petrera54,44 , J. Phuntsok92 , R. Piegaia3 ,
T. Pierog36 , P. Pieroni3 , M. Pimenta71 , V. Pirronello55,43 , M. Platino8 , M. Plum38 ,
C. Porowski69 , R.R. Prado15 , P. Privitera93 , M. Prouza25 , E.J. Quel2 , S. Querchfeld34 ,
S. Quinn82 , J. Rautenberg34 , O. Ravel33 , D. Ravignani8 , D. Reinert38 , B. Revenu33 ,
J. Ridky25 , M. Risse40 , P. Ristori2 , V. Rizi54,44 , W. Rodrigues de Carvalho81 ,
J. Rodriguez Rojo9 , M.D. Rodrı́guez-Frı́as79 , D. Rogozin36 , J. Rosado78 , M. Roth36 ,
E. Roulet1 , A.C. Rovero5 , S.J. Saffi12 , A. Saftoiu72 , H. Salazar59 , A. Saleh77 ,
F. Salesa Greus92 , G. Salina48 , J.D. Sanabria Gomez24 , F. Sánchez8 , P. SanchezLucas80 , E.M. Santos16 , E. Santos17 , F. Sarazin83 , B. Sarkar34 , R. Sarmento71 ,
C. Sarmiento-Cano24 , R. Sato9 , C. Scarso9 , M. Schauer34 , V. Scherini53,45 , H. Schieler36 ,
D. Schmidt36 , O. Scholten66,c , H. Schoorlemmer94 , P. Schovánek25 , F.G. Schröder36 ,
A. Schulz36 , J. Schulz65 , J. Schumacher38 , A. Segreto41,43 , M. Settimo30 , A. Shadkam87 ,
R.C. Shellard13 , G. Sigl39 , O. Sima74 , A. Śmialkowski70 , R. Šmı́da36 , G.R. Snow95 ,
P. Sommers92 , S. Sonntag40 , J. Sorokin12 , R. Squartini9 , D. Stanca72 , S. Stanič77 ,
J. Stapleton91 , J. Stasielak69 , M. Stephan38 , F. Strafella53,45 , A. Stutz31 , F. Suarez8,11 ,
M. Suarez Durán24 , T. Suomijärvi28 , A.D. Supanitsky5 , M.S. Sutherland91 ,
J. Swain90 , Z. Szadkowski70 , O.A. Taborda1 , A. Tapia8 , A. Tepe40 , V.M. Theodoro17 ,
C. Timmermans67,65 , C.J. Todero Peixoto14 , G. Toma72 , L. Tomankova36 , B. Tomé71 ,
A. Tonachini51,49 , G. Torralba Elipe81 , D. Torres Machado22 , P. Travnicek25 ,
M. Trini77 , R. Ulrich36 , M. Unger89,36 , M. Urban38 , J.F. Valdés Galicia64 , I. Valiño81 ,
L. Valore57,47 , G. van Aar65 , P. van Bodegom12 , A.M. van den Berg66 , A. van Vliet65 ,
E. Varela59 , B. Vargas Cárdenas64 , G. Varner94 , R. Vasquez22 , J.R. Vázquez78 ,
R.A. Vázquez81 , D. Veberič36 , V. Verzi48 , J. Vicha25 , M. Videla8 , L. Villaseñor63 ,
S. Vorobiov77 , H. Wahlberg4 , O. Wainberg8,11 , D. Walz38 , A.A. Watsona , M. Weber37 ,
K. Weidenhaupt38 , A. Weindl36 , L. Wiencke83 , H. Wilczyński69 , T. Winchen34 ,
D. Wittkowski34 , B. Wundheiler8 , S. Wykes65 , L. Yang77 , T. Yapici88 , A. Yushkov40 ,
E. Zas81 , D. Zavrtanik77,76 , M. Zavrtanik76,77 , A. Zepeda60 , B. Zimmermann37 ,
M. Ziolkowski40 , Z. Zong28 , F. Zuccarello55,43
1 Centro Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET),
Argentina
2 Centro de Investigaciones en Láseres y Aplicaciones, CITEDEF and CONICET,
Argentina
– 32 –
3
Departamento de Fı́sica, FCEyN, Universidad de Buenos Aires, Argentina
IFLP, Universidad Nacional de La Plata and CONICET, Argentina
5 Instituto de Astronomı́a y Fı́sica del Espacio (IAFE, CONICET-UBA), Argentina
6 Instituto de Fı́sica de Rosario (IFIR) – CONICET/U.N.R. and Facultad de Ciencias
Bioquı́micas y Farmacéuticas U.N.R., Argentina
7 Instituto de Tecnologı́as en Detección y Astropartı́culas (CNEA, CONICET,
UNSAM) and Universidad Tecnológica Nacional – Facultad Regional Mendoza (CONICET/CNEA), Argentina
8 Instituto de Tecnologı́as en Detección y Astropartı́culas (CNEA, CONICET, UNSAM),
Centro Atómico Constituyentes, Comisión Nacional de Energı́a Atómica, Argentina
9 Observatorio Pierre Auger, Argentina
10 Observatorio Pierre Auger and Comisión Nacional de Energı́a Atómica, Argentina
11 Universidad Tecnológica Nacional – Facultad Regional Buenos Aires, Argentina
12 University of Adelaide, Australia
13 Centro Brasileiro de Pesquisas Fisicas (CBPF), Brazil
14 Universidade de São Paulo, Escola de Engenharia de Lorena, Brazil
15 Universidade de São Paulo, Inst. de Fı́sica de São Carlos, São Carlos, Brazil
16 Universidade de São Paulo, Inst. de Fı́sica, São Paulo, Brazil
17 Universidade Estadual de Campinas (UNICAMP), Brazil
18 Universidade Estadual de Feira de Santana (UEFS), Brazil
19 Universidade Federal da Bahia, Brazil
20 Universidade Federal de Pelotas, Brazil
21 Universidade Federal do ABC (UFABC), Brazil
22 Universidade Federal do Rio de Janeiro (UFRJ), Instituto de Fı́sica, Brazil
23 Universidade Federal Fluminense, Brazil
24 Universidad Industrial de Santander, Colombia
25 Institute of Physics (FZU) of the Academy of Sciences of the Czech Republic, Czech
Republic
26 Palacky University, RCPTM, Czech Republic
27 University Prague, Institute of Particle and Nuclear Physics, Czech Republic
28 Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris 11, CNRS-IN2P3,
France
29 Laboratoire de l’Accélérateur Linéaire (LAL), Université Paris 11, CNRS-IN2P3,
France
30 Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Universités Paris
6 et Paris 7, CNRS-IN2P3, France
31 Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Université GrenobleAlpes, CNRS/IN2P3, France
32 Station de Radioastronomie de Nançay, France
33 SUBATECH, École des Mines de Nantes, CNRS-IN2P3, Université de Nantes, France
34 Bergische Universität Wuppertal, Fachbereich C – Physik, Germany
35 Karlsruhe Institute of Technology, Institut für Experimentelle Kernphysik (IEKP),
Germany
4
– 33 –
36
Karlsruhe Institute of Technology, Institut für Kernphysik (IKP), Germany
Karlsruhe Institute of Technology, Institut für Prozessdatenverarbeitung und Elektronik (IPE), Germany
38 RWTH Aachen University, III. Physikalisches Institut A, Germany
39 Universität Hamburg, II. Institut für Theoretische Physik, Germany
40 Universität Siegen, Fachbereich 7 Physik – Experimentelle Teilchenphysik, Germany
41 INAF – Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo, Italy
42 INFN Laboratori del Gran Sasso, Italy
43 INFN, Sezione di Catania, Italy
44 INFN, Sezione di L’Aquila, Italy
45 INFN, Sezione di Lecce, Italy
46 INFN, Sezione di Milano, Italy
47 INFN, Sezione di Napoli, Italy
48 INFN, Sezione di Roma ”Tor Vergata”, Italy
49 INFN, Sezione di Torino, Italy
50 Osservatorio Astrofisico di Torino (INAF), Torino, Italy
51 Università Torino, Dipartimento di Fisica, Italy
52 Università del Salento, Dipartimento di Ingegneria, Italy
53 Università del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”, Italy
54 Università dell’Aquila, Dipartimento di Chimica e Fisica, Italy
55 Università di Catania, Dipartimento di Fisica e Astronomia, Italy
56 Università di Milano, Dipartimento di Fisica, Italy
57 Università di Napoli ”Federico II”, Dipartimento di Fisica, Italy
58 Università di Roma “Tor Vergata”, Dipartimento di Fisica, Italy
59 Benemérita Universidad Autónoma de Puebla (BUAP), México
60 Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV), México
61 Unidad Profesional Interdisciplinaria en Ingenierı́a y Tecnologı́as Avanzadas del
Instituto Politécnico Nacional (UPIITA-IPN), México
62 Universidad Autónoma de Chiapas, México
63 Universidad Michoacana de San Nicolás de Hidalgo, México
64 Universidad Nacional Autónoma de México, México
65 Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud
Universiteit, Nijmegen, Netherlands
66 KVI – Center for Advanced Radiation Technology, University of Groningen, Netherlands
67 Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Netherlands
68 Stichting Astronomisch Onderzoek in Nederland (ASTRON), Dwingeloo, Netherlands
69 Institute of Nuclear Physics PAN, Poland
70 University of Lódź, Poland
71 Laboratório de Instrumentação e Fı́sica Experimental de Partı́culas – LIP and Instituto
Superior Técnico – IST, Universidade de Lisboa – UL, Portugal
72 “Horia Hulubei” National Institute for Physics and Nuclear Engineering, Romania
73 Institute of Space Science, Romania
37
– 34 –
74
University of Bucharest, Physics Department, Romania
University Politehnica of Bucharest, Romania
76 Experimental Particle Physics Department, J. Stefan Institute, Slovenia
77 Laboratory for Astroparticle Physics, University of Nova Gorica, Slovenia
78 Universidad Complutense de Madrid, Spain
79 Universidad de Alcalá de Henares, Spain
80 Universidad de Granada and C.A.F.P.E., Spain
81 Universidad de Santiago de Compostela, Spain
82 Case Western Reserve University, USA
83 Colorado School of Mines, USA
84 Colorado State University, USA
85 Department of Physics and Astronomy, Lehman College, City University of New York,
USA
86 Fermi National Accelerator Laboratory, USA
87 Louisiana State University, USA
88 Michigan Technological University, USA
89 New York University, USA
90 Northeastern University, USA
91 Ohio State University, USA
92 Pennsylvania State University, USA
93 University of Chicago, USA
94 University of Hawaii, USA
95 University of Nebraska, USA
96 University of New Mexico, USA
a School of Physics and Astronomy, University of Leeds, Leeds, United Kingdom
b Max-Planck-Institut für Radioastronomie, Bonn, Germany
c also at Vrije Universiteit Brussels, Brussels, Belgium
d also at Universidade Federal do Paraná, Palotina, PR, Brazil
75
– 35 –
The Telescope Array Collaboration
R.U. Abbasi1 , M. Abe2 , T. Abu-Zayyad1 , M. Allen1 , R. Azuma3 , E. Barcikowski1 ,
J.W. Belz1 , D.R. Bergman1 , S.A. Blake1 , R. Cady1 , M.J. Chae4 , B.G. Cheon5 ,
J. Chiba6 , M. Chikawa7 , W.R. Cho8 , T. Fujii9 , M. Fukushima9,10 , T. Goto11 ,
W. Hanlon1 , Y. Hayashi11 , N. Hayashida12 , K. Hibino12 , K. Honda13 , D. Ikeda9 ,
N. Inoue2 , T. Ishii13 , R. Ishimori3 , H. Ito14 , D. Ivanov1 , C.C.H. Jui1 , K. Kadota15 ,
F. Kakimoto3 , O. Kalashev16 , K. Kasahara17 , H. Kawai18 , S. Kawakami11 , S. Kawana2 ,
K. Kawata9 , E. Kido9 , H.B. Kim5 , J.H. Kim1 , J.H. Kim19 , S. Kitamura3 , Y. Kitamura3 ,
V. Kuzmin16,† , Y.J. Kwon8 , J. Lan1 , S.I. Lim4 , J.P. Lundquist1 , K. Machida13 ,
K. Martens10 , T. Matsuda20 , T. Matsuyama11 , J.N. Matthews1 , M. Minamino11 ,
Y. Mukai13 , I. Myers1 , K. Nagasawa2 , S. Nagataki14 , T. Nakamura21 , T. Nonaka9 ,
A. Nozato7 , S. Ogio11 , J. Ogura3 , M. Ohnishi9 , H. Ohoka9 , K. Oki9 , T. Okuda22 ,
M. Ono23 , A. Oshima24 , S. Ozawa17 , I.H. Park25 , M.S. Pshirkov16,26 , D.C. Rodriguez1 ,
G. Rubtsov16 , D. Ryu19 , H. Sagawa9 , N. Sakurai11 , L.M. Scott27 , P.D. Shah1 ,
F. Shibata13 , T. Shibata9 , H. Shimodaira9 , B.K. Shin5 , H.S. Shin9 , J.D. Smith1 ,
P. Sokolsky1 , R.W. Springer1 , B.T. Stokes1 , S.R. Stratton1,27 , T.A. Stroman1 ,
T. Suzawa2 , M. Takamura6 , M. Takeda9 , R. Takeishi9 , A. Taketa28 , M. Takita9 ,
Y. Tameda12 , H. Tanaka11 , K. Tanaka29 , M. Tanaka20 , S.B. Thomas1 , G.B. Thomson1 ,
P. Tinyakov30,16 , I. Tkachev16 , H. Tokuno3 , T. Tomida31 , S. Troitsky16 , Y. Tsunesada3 ,
K. Tsutsumi3 , Y. Uchihori32 , S. Udo12 , F. Urban30 , G. Vasiloff1 , T. Wong1 , R. Yamane11 ,
H. Yamaoka20 , K. Yamazaki28 , J. Yang4 , K. Yashiro6 , Y. Yoneda11 , S. Yoshida18 ,
H. Yoshii33 , R. Zollinger1 , Z. Zundel1
1 High Energy Astrophysics Institute and Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah, USA
2 The Graduate School of Science and Engineering, Saitama University, Saitama,
Saitama, Japan
3 Graduate School of Science and Engineering, Tokyo Institute of Technology, Meguro,
Tokyo, Japan
4 Department of Physics and Institute for the Early Universe, Ewha Womans University,
Seodaaemun-gu, Seoul, Korea
5 Department of Physics and The Research Institute of Natural Science, Hanyang University, Seongdong-gu, Seoul, Korea
6 Department of Physics, Tokyo University of Science, Noda, Chiba, Japan
7 Department of Physics, Kinki University, Higashi Osaka, Osaka, Japan
8 Department of Physics, Yonsei University, Seodaemun-gu, Seoul, Korea
9 Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba, Japan
10 Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, the University of Tokyo, Kashiwa, Chiba, Japan
11 Graduate School of Science, Osaka City University, Osaka, Osaka, Japan
12 Faculty of Engineering, Kanagawa University, Yokohama, Kanagawa, Japan
13 Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, Kofu, Yamanashi, Japan
14 Astrophysical Big Bang Laboratory, RIKEN, Wako, Saitama, Japan
– 36 –
15
Department of Physics, Tokyo City University, Setagaya-ku, Tokyo, Japan
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia
17 Advanced Research Institute for Science and Engineering, Waseda University,
Shinjuku-ku, Tokyo, Japan
18 Department of Physics, Chiba University, Chiba, Chiba, Japan
19 Department of Physics, School of Natural Sciences, Ulsan National Institute of Science and Technology, UNIST-gil, Ulsan, Korea
20 Institute of Particle and Nuclear Studies, KEK, Tsukuba, Ibaraki, Japan
21 Faculty of Science, Kochi University, Kochi, Kochi, Japan
22 Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga, Japan
23 Department of Physics, Kyushu University, Fukuoka, Fukuoka, Japan
24 Engineering Science Laboratory, Chubu University, Kasugai, Aichi, Japan
25 Department of Physics, Sungkyunkwan University, Jang-an-gu, Suwon, Korea
26 Sternberg Astronomical Institute, Moscow M.V. Lomonosov State University,
Moscow, Russia
27 Department of Physics and Astronomy, Rutgers University – The State University of
New Jersey, Piscataway, New Jersey, USA
28 Earthquake Research Institute, University of Tokyo, Bunkyo-ku, Tokyo, Japan
29 Graduate School of Information Sciences, Hiroshima City University, Hiroshima, Hiroshima, Japan
30 Service de Physique Théorique, Université Libre de Bruxelles, Brussels, Belgium
31 Department of Computer Science and Engineering, Shinshu University, Nagano,
Nagano, Japan
32 National Institute of Radiological Science, Chiba, Chiba, Japan
33 Department of Physics, Ehime University, Matsuyama, Ehime, Japan
† Deceased
16
– 37 –
Table 4. List of the neutrino cascade-like events used in the analyses. The ID number corresponds to the ID in [21, 22]. ‘Dep. Energy’ corresponds to the EM equivalent energy deposited
within the detector.
ID
1
2
4
6
7
9
10
11
12
14
15
16
17
19
20
21
22
24
25
26
27
29
30
31
33
34
35
36
39
40
41
42
46
48
49
50
51
52
54
Dep. Energy [TeV]
47.6+6.5
−5.4
117+15
−15
165+20
−15
28.4+2.7
−2.5
34.3+3.5
−4.3
63.2+7.1
−8.0
97.2+10.4
−12.4
88.4+12.5
−10.7
104+13
−13
1041+132
−144
57.5+8.3
−7.8
30.6+3.6
−3.5
200+27
−27
71.5+7.0
−7.2
1141+143
−133
30.2+3.5
−3.3
220+21
−24
30.5+3.2
−2.6
33.5+4.9
−5.0
210+29
−26
60.2+5.6
−5.6
32.7+3.2
−2.9
129+14
−12
42.5+5.4
−5.7
385+46
−49
42.1+6.5
−6.3
2004+236
−262
28.9+3.0
−2.6
101.3+13.3
−11.6
157.3+15.9
−16.7
87.6+8.4
−10.0
76.3+10.3
−11.6
158.0+15.3
−16.6
104.7+13.5
−10.2
59.9+8.3
−7.9
22.2+2.3
−2.0
66.2+6.7
−6.1
158.1+16.3
18.4
54.5+5.1
−6.3
RA [◦ ]
35.2
282.6
169.5
133.9
15.6
151.3
5.0
155.3
296.1
265.6
287.3
192.1
247.4
76.9
38.3
9.0
293.7
282.2
286.0
143.4
121.7
298.1
103.2
146.1
292.5
323.4
208.4
257.7
106.2
143.9
66.1
42.5
150.5
213.1
203.2
168.6
88.6
252.8
170.5
dec [◦ ]
-1.8
-28.0
-51.2
-27.2
-45.1
33.6
-29.4
-8.9
-52.8
-27.9
-49.7
-22.6
14.5
-59.7
-67.2
-24.0
-22.1
-15.1
-14.5
22.7
-12.6
41.0
-82.7
78.3
7.8
31.3
-55.8
-3.0
-17.9
-48.5
3.3
-25.3
-22.4
-33.2
-26.3
59.3
54.0
-54.0
6.0
– 38 –
Med. Angular Error [◦ ]
16.3
25.4
7.1
9.8
24.1
16.5
8.1
16.7
9.8
13.2
19.7
19.4
11.6
9.7
10.7
20.9
12.1
15.5
46.3
11.8
6.6
7.4
8.0
26.0
13.5
42.7
15.9
11.7
14.2
11.7
11.1
20.7
7.6
8.1
21.8
8.2
6.5
7.8
11.6
Table 5. List of the neutrino track-like events used in the analyses. The first seven ID numbers
correspond to the IDs in [21, 22]. The rest of the ID numbers correspond to the high-energy
tracks from [23] described in Section 2.1.2. For these events, the ‘most probable muon energy’
is an estimate of the muon energy assuming the best fit spectrum resulting from the flux fit in
that analysis [23], which is different from the deposited energy specified for HESE tracks and
cascades.
ID
5
13
23
38
44
45
47
ID
116357,6324295
116807,9493609
119136,66932419
116883,17395151
116701,6581938
116026,44241207
116574,20123342
119739,41603205
118210,47538807
Dep. Energy [TeV]
71.4+9.0
−9.0
253+26
−22
82.2+8.6
−8.4
200.5+16.4
−16.4
84.6+7.4
−7.9
429.9+57.4
−49.1
74.3+8.3
−7.2
Most probable muon energy [TeV]
755
604
397
422
317
339
302
326
252
– 39 –
RA [◦ ]
110.6
67.9
208.7
93.3
336.7
219.0
209.4
RA [◦ ]
254 .0
88.5
37.1
285.7
331 .0
346.8
267.5
238.3
235.2
dec [◦ ]
-0.4
40.3
-13.2
14.0
0.0
-86.3
67.4
dec [◦ ]
16.3
0.2
18.6
3.1
11.0
24.0
13.8
18.9
19.3
Med. Angular Error [◦ ]
. 1.2
. 1.2
. 1.9
. 1.2
. 1.2
. 1.2
. 1.2
Med. Angular Error [◦ ]
. 1.0
. 1.0
. 1.0
. 1.0
. 1.0
. 1.0
. 1.0
. 1.0
. 1.0

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